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Res

Syntax

Res(M):TAGGED("$gb.Res")

where M is of type IDEAL or MODULE or TAGGED("Quotient").
    

Summary

free resolution

Description

This function returns the minimal free resolution of M. If M is a quotient of the current ring by an ideal I or a quotient of a free module by a submodule N, then the resolution of M is defined to be that of I or N, respectively.

Res only works in the homogeneous context, and the coefficient ring must be a field.

example

    
Use R ::= Q[x,y,z];
I := Ideal(x,y,z^2);
Res(R/I);
0 --> R(-4) --> R(-2)(+)R^2(-3) --> R^2(-1)(+)R(-2) --> R
-------------------------------
Describe It;

Mat[
  [y, x, z^2]
]
Mat[
  [x, z^2, 0],
  [-y, 0, z^2],
  [0, -y, -x]
]
Mat[
  [z^2],
  [-x],
  [y]
]
-------------------------------

For fine control and monitoring of Groebner basis calculations,
including various types of truncations, see "The Interactive Groebner
Framework" and "Introduction to Panels".
        
    

See Also